Geometry
Purpose of Course showclose
“Everything is numbers.” This phrase was uttered by the lead character, Dr. Charlie Epps, on the hit television show “NUMB3RS.” If everything has a mathematical underpinning, then it follows that everything is somehow mathematically connected, even if it is only in some odd, “six degrees of separation (or Kevin Bacon)” kind of way.
Geometry is the study of space (for now, mainly twodimensional, with some threedimensional thrown in) and the relationships of objects contained inside. It is one of the more relatable math courses, because it often answers that ageold question, “When am I ever going to use this in real life?” Look around you right now. Do you see any triangles? Can you spot any circles? Do you see any books that look like they are twice the size of other books? Does your wall have paint on it?
In geometry, you will explore the objects that make up our universe. Most people never give a second thought to how things are constructed, but there are geometric rules at play. Most people never think twice about a rocket launch, but if that rocket is not launched at an exact angle, it will miss its target. A football field has to be measured out to be a rectangle; if you used another shape, such as a trapezoid, that would give an unfair advantage to one team, because that one team would have more space to work with.
In this course, you will study the relationships between lines and angles. Have you ever looked at a street map? Believe it or not, there is a lot of geometry on a map, as you will see from this course. You will learn to calculate how much space an object covers, which is useful if you ever have to, say, buy some paint. You will learn to determine how much space is inside of a threedimensional object, which is useful for those times you are trying to fit four suitcases, three kids, two adults, and a dog into the back of your vehicle.
These are just some of the topics you will be learning. As you will quickly see, everything is not just numbers; it is also relationships. Even nature itself knows this. What did the little acorn say when it grew up? “Gee, I’m a tree!”
Course Information showclose
Course Designer: Eric Clark
Primary Resources: This course is composed of a range of different free, online materials. However, the course makes primary use of the following materials:
 Salman Khan’s Khan Academy Mathematics Videos
 CK12: Geometry
 CK12 Flexbook: Victor Cifarelli et al.’s Geometry
 Subunit 1.1 Assessment
 Subsubunit 1.4.4 Assessment
 Subsubunit 1.4.5 Assessment
 Subsubunit 1.4.7 Assessment
 Subsubunit 2.2.5 Assessment
 Subunit 3.1 Assessment
 Subsubunit 3.2.3 Assessment
 Subsubunit 3.3.5 Assessment
 Subsubunit 4.6.2 Assessment
 Subunit 5.2 Assessment
 Subunit 5.7 Assessment
 Subunit 6.1 Assessment
 Subunit 6.3 Assessment
 Subunit 7.1 Assessment
 Subunit 7.3 Assessment
 Subunit 7.4 Assessment
 Subunit 9.2 Assessment
 Subunit 9.3 Assessment
 Subunit 9.6 Assessment
 Subunit 9.10 Assessment
 Subunit 10.7 Assessment
 The Final Exam
In order to pass this course, you will need to earn a 70% or higher on the Final Exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: This course should take you approximately a total of 144.75 hours to complete. Each unit includes a “time advisory” that lists the amount of time you are expected to spend on each subunit. It may be useful to take a look at these time advisories and determine how much time you have over the next few weeks to complete each unit and to then set goals for yourself. For example, Unit 1 should take you 17.5 hours. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 3 hours) on Monday night; subunits 1.2 and 1.3 (a total of 2.25 hours) on Tuesday night; etc.
Tips/Suggestions: Please make sure to take comprehensive notes as you work through each resource. These notes will serve as a useful review as you study for your Final Exam. Complete all practice problems, because practice will allow you to fully understand each concept.
This course features a number of Khan Academy™ videos. Khan Academy™ has a library of over 3,000 videos covering a range of topics (math, physics, chemistry, finance, history and more), plus over 300 practice exercises. All Khan Academy™ materials are available for free at www.khanacademy.org.

Learning Outcomes showclose
Upon successful completion of this course, the student will be able to:
 Define and identify angles, rays, line segments, and points, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. (HSGCO.A.1)
 Use the definition of congruence to decide if figures are congruent. (HSGCO.B.6)
 Use the definition of congruence to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. (HSGCO.B.7)
 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence. (HSGCO.B.8)
 Given two figures, decide if they are similar. (HSGSRT.A.2)
 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (HSGSRT.A.3)
 Explain and use the relationship between the sine and cosine of complementary angles. (HSGSRT.C.7)
 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. (HSGSRT.C.8)
 Identify and describe relationships among inscribed angles, radii, and chords. (HSGC.A.2)
 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.(HSGGMD.A.3)
 Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. (HSGGMD.B.4)
 Use geometric shapes, their measures, and their properties to describe objects. (HSGMG.A.1)
 Recall the formulas for the area and circumference of a circle and use them to solve problems. (7.G.B.4)
 Using facts about supplementary, complementary, vertical, and adjacent angles, write and solve simple equations for an unknown angle in a figure. (7.G.B.5)
 Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (7.G.B.6)
Course Requirements showclose
√ have access to a computer.
√ have continuous broadband Internet access.
√ have the ability/permission to install plugins or software (e.g. Adobe Reader or Flash).
√ have the ability to download and save files and documents to a computer.
√ have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.).
√ have competency in the English language.
√ have read the Saylor Student Handbook.
√ have completed courses RWM101: Real World Math I: Foundations and RWM102: Real World Math II: Algebra.
Preliminary Information

Course Materials
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry (PDF)
Instructions: Many resources in this course will reference this textbook. For convenience sake, unit resources that make use of this book will link directly to the appropriate section of the online HTML version. However, you may download the full text at the link above and refer to it throughout the course if you wish to have offline access. You can access the online version of the textbook here (HTML).
Terms of Use: The above textbook is released under a Creative Commons Attribution NonCommercial Share Alike 3.0 License (CCBYNCSA). It is attributed to the CK12 Foundation.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry
Unit Outline show close

Unit 1: Basics of Geometry
From a young age, we learn basic vocabulary and basic concepts that lead us to understand greater concepts. In this unit, you will learn about the basic building blocks of Geometry.
Time Advisory show close
Everything has a proper name. We often seem to use nicknames: “fridge” instead of “refrigerator,” “phone” instead of “telephone,” and so on. Still, we know what the proper terminology is, even if we do not use it as often as we probably should. Knowing the meanings of several basic terms in Geometry is important, because these terms are going to keep popping up over and over again. Whether it is knowing a simple definition, or understanding the relationships between angles, these basic items are a “must know” in Geometry.
In life, we also classify things. We tend to classify by height, age, weight, food preference, nationality, etc. We will use pretty much anything we can think of for classification purposes. While some classifications might seem unnecessary to us, others seem quite important. Classifying berries, for example, can help you to keep from eating a poisonous one that would make you sick. Without classification, we would not have a way to keep the good ones separate from the bad ones. The same holds true in Geometry. Classifying shapes like triangles can help us recognize these shapes faster and eventually recognize the rules and relationships pertaining to their classification.
Learning Outcomes show close

1.1 Language and Notation of Basic Geometry
 Lecture: Khan Academy’s “Language and Notation of Basic Geometry”
Link: Khan Academy’s “Language and Notation of Basic Geometry” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to learn about the language and notation of basic geometry including line, line segment, ray, midpoint, collinear, and planar. Watch the presentation carefully two or three times until you are able to explain how to understand the terminology and notation associated with these terms.
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: Khan Academy’s “Lines, Line Segments, and Rays”
Link: Khan Academy’s “Lines, Line Segments, and Rays” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to learn about how to identify the differences between a line, line segment, and a ray. Watch the presentation carefully two or three times until you are able to explain how to understand the differences with these terms.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Points, Lines, and Planes”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Points, Lines, and Planes” (PDF)
Instructions: Please click on the link above and complete questions 1–10 (“Lesson Exercises” Pages 9 and 10 in the textbook). These questions will provide you with the opportunity to identify general geometry terms and draw diagrams. The solutions to these problems are located in the “Answers” section, (starting on page 10 of the textbook).
This activity should take approximately 15 minutes to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Points, Lines, and Planes” and “Recognizing Rays, Lines, and Line Segments”
Link: Khan Academy’s “Points, Lines, and Planes” (HTML) and “Recognizing Rays, Lines, and Line Segments” (HTML)
Instructions: Please click on the links above, and complete the assessments that test your knowledge on basic geometry terminology. You can review the concepts associated with these questions with the Khan videos in subunit 1.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
This assessment will take approximately 1 hour to complete.
Terms of Use: These resources are licensed under a Creative Commons AttributionShareAlike License 3.0. They are attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Points, Lines, and Planes”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Points, Lines, and Planes” (PDF)
Instructions: Please click on the link above and study the “Points, Lines, and Planes” section (Pages 1–9 in the textbook), stopping at “Review Questions.” This section provides examples and definitions of point, line, plane, space, segment rays, postulates, and draw diagrams.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Language and Notation of Basic Geometry”

1.2 Distance between Two Points
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance between Two Points”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance between Two Points” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the embedded videos to learn about the distance between two points and the segment addition postulate. Watch the presentations carefully two or three times until you are able to explain how apply finding the distance between two points and the segment addition postulate. Then, read the following sections: “Guidance” (omitting the Distance between Two Points B video), “Vocabulary,” and “Guided Practice.” This section provides examples of measuring on a ruler and finding the distance between points. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Watching these videos, reading the material, and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance between Two Points”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance between Two Points” (HTML)
Instructions: Please click on the link above, select the “Exercises” tab, and complete the activity on the distance between two points and the angle addition postulate. Compute the answer to the given problem, and select your response. Click on “Submit Answer” to see if you choose the correct or an incorrect answer. Then, click on “Next” to move on to another question. You have completed the activity when you see “You have reached the maximum practice questions.” (Note: You can refresh the page if you would like additional practice problems and the questions will be different than the first set.) You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance between Two Points”

1.3 Midpoints and Segment Bisectors
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midpoints and Segment Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midpoints and Segment Bisectors” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first two videos (5 minutes and 7 minutes, respectively) to learn about midpoints and segment bisectors. You do not need to watch the “James Sousa: Segment Midpoint and Segment Perpendicular Bisector” video. Watch the presentations carefully two or three times until you are able to explain how apply the segment addition postulate. Then, read the following sections: “Guidance” (omitting the Midpoints and Segment Bisectors B video), “Vocabulary,” and “Guided Practice.” This section provides examples of measuring on a ruler and finding the distance between points. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Watching this lecture, reading the material, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midpoints and Segment Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midpoints and Segment Bisectors” (HTML and YouTube)
Instructions: Please click on the link above, select the “Exercises” tab, and complete the activity on the midpoints and segment bisectors. Compute the answer to the given problem, and select your response. Click on “Submit Answer” to see if you choose the correct or an incorrect answer. Then, click on “Next” to move on to another question. You have completed the activity when you see “You have reached the maximum practice questions.” (Note: You can refresh the page if you would like additional practice problems and the questions will be different than the first set.) You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midpoints and Segment Bisectors”
 1.4 Angles

1.4.1 Angle Basics
 Lecture: Khan Academy’s “Angle Basics”
Link: Khan Academy’s “Angle Basics” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to learn about the language and notation of angles. Watch the presentation carefully two or three times until you are able to explain how to understand the terminology and notation associated with these terms.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Angle Basics”

1.4.2 Measuring Angles
 Lecture: Khan Academy’s “Using a Protractor” and “Measuring Angles in Degrees”
Link: Khan Academy’s “Using a Protractor” (YouTube) and “Measuring Angles in Degrees” (YouTube)
Instructions: Please click on the links above, and take notes as you watch these videos to learn about how to use a protractor and to measure angles in degrees. Watch the presentations carefully two or three times until you are able to measure an angle with a protractor and measuring angles in degrees.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: These resources are licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. They are attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Measurement”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Measurement” (HTML)
Instructions: Please click on the link above and read the following sections: “Guidance,” “Vocabulary,” and “Guided Practice.” This section provides examples of measuring with a protractor and understanding the angle addition postulate. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading these sections and taking notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Measurement”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Measurement” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–17. These exercises will provide you with the opportunity to use the angle addition postulate, properties of angles, and draw and measure angles with a protractor. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Angle Measurement Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Using a Protractor” and “Measuring Angles in Degrees”

1.4.3 Congruent Angles and Angle Bisectors
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Angles and Angle Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Angles and Angle Bisectors” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first two videos (approximately 5 minutes and 3 minutes, respectively) to learn about angle bisectors. You do not need to watch the “James Sousa: Bisector and Midpoint Exercises” video. Watch the presentation carefully two or three times until you are able to understand problems with an angle bisector. Then, read the following sections: “Guidance” (omitting Congruent Angles and Angle Bisectors B video), “Vocabulary,” and “Guided Practice.” This section provides examples identifying congruent angles and applying properties of an angle bisector. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Watching this lecture, reading the sections, and pausing to take notes should take no more than 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Angles and Angle Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Angles and Angle Bisectors” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–10. These exercises will provide you with the opportunity to use properties of congruent angles and angle bisectors. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Congruent Angles and Angle Bisectors Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Angles and Angle Bisectors”

1.4.4 Acute, Obtuse, and Right Angles
 Lecture: Khan Academy’s “Acute, Right, and Obtuse Angles” and “Measuring Angles in Degrees”
Link: Khan Academy’s “Acute, Right, and Obtuse Angles” (YouTube) and “Measuring Angles in Degrees” (YouTube)
Instructions: Please click on the links above, and take notes as you watch these videos to learn how to identify acute, right, and obtuse angles. Watch the presentations carefully two or three times until you are able to identify types of angles.
Watching these lectures and pausing to take notes should take no more than 1 hour.
Terms of Use: These resources are licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. They are attributed to the Khan Academy.  Assessment: Khan Academy’s “Angle Types”
Link: Khan Academy’s “Angle Types” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on types of angles. You can review the concepts associated with these questions with the Khan videos in subsubunit 1.4.4. Determine if the given angle is acute, right, or obtuse using the interactive protractor. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Acute, Right, and Obtuse Angles” and “Measuring Angles in Degrees”

1.4.5 Complementary and Supplementary Angles
 Lecture: Khan Academy’s “Complementary and Supplementary Angles” and “Identifying Complementary and Supplementary Angles”
Link: Khan Academy’s “Complementary and Supplementary Angles” (YouTube) and “Identifying Complementary and Supplementary Angles” (YouTube)
Instructions: Please click on the links above, and take notes as you watch these videos to learn how to identify supplementary and complementary angles. Watch the first presentation carefully to understand the basics of complementary, supplementary, adjacent, and straight angles. Watch the second presentations carefully two or three times until you are able to identify types of angles.
Watching these lectures and pausing to take notes should take no more than 1 hour.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. They are attributed to the Khan Academy.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Complementary Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Complementary Angles” (HTML)
Instructions: Please click on the link above, select the “Exercises” tab, and complete the problems on complementary angles. Compute the answer to the given problem, and select your response. Then, click “Submit Answer” to see if you chose the correct answer or an incorrect answer. Select “Next” to move on to another question. You have completed the activity when you see “You have reached the maximum practice questions.” (Note: You can refresh the page if you would like additional practice problems and the questions will be different than the first set.) You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Supplementary Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Supplementary Angles” (HTML)
Instructions: Please click on the link above, select the “Exercises” tab, and complete the problems on supplementary angles. Compute the answer to the given problem, and select your response. Click on “Submit Answer” to see if you chose the correct answer or an incorrect answer. Select “Next” to move on to another question. You have completed the activity when you see “You have reached the maximum practice questions.” (Note: You can refresh the page if you would like additional practice problems and the questions will be different than the first set.) You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Completing this interactive lab should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Complementary and Supplementary Angles”
Link: Khan Academy’s “Complementary and Supplementary Angles” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on complementary and supplementary angles. You can review the concepts associated with these questions with the Khan videos in subsubunit 1.4.5. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Complementary and Supplementary Angles” and “Identifying Complementary and Supplementary Angles”

1.4.6 Linear Pairs
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Linear Pairs”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Linear Pairs” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about linear pairs. You do not need to watch the “James Sousa: Linear Pairs” video. Watch the presentation carefully two or three times until you are able to understand problems with linear pairs. Then, read the following sections: “Guidance” (omitting Linear Pairs B video), “Vocabulary,” and “Guided Practice.” This section provides examples of adjacent angles and angles that form a linear pair. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Watching this video, reading the material, and pausing to take notes will take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Linear Pairs”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Linear Pairs” (HTML and YouTube)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–16. These exercises will provide you with the opportunity to determine angles using linear pairs. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Linear Pairs Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Linear Pairs”

1.4.7 Vertical Angles
 Lecture: Khan Academy’s “Angles at the Intersection of Two Lines”
Link: Khan Academy’s “Angles at the Intersection of Two Lines” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to learn how vertical angles are equal to each other. Watch the presentation carefully two or three times to understand how vertical angles are equal.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Vertical Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Vertical Angles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video (approximately 3 minutes) to learn about linear pairs. You do not need to watch the “James Sousa: Vertical Angles” video. Watch the presentation carefully two or three times until you are able to understand problems with vertical angles. Then, read the following sections: “Guidance” (omitting Vertical Angles B video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of vertical angles and the vertical angles theorem. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the video, and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Vertical Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Vertical Angles” (HTML and YouTube)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to determine angles using vertical angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Vertical Angles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Khan Academy’s “Vertical Angles 2”
Link: Khan Academy’s “Vertical Angles 2” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on vertical angles. You can review the concepts associated with these questions with the Khan videos in subsubunit 1.4.7. Determine the value for the problem and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Angles at the Intersection of Two Lines”

1.5 Polygon Classification
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Classifying Polygons”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Classifying Polygons” (HTML)
Instructions: Please click on the link above and study the “Points, Lines, and Planes” section (Pages 49–54 in the textbook), stopping at “Using the Distance Formula on Polygons.” This section provides examples of various polygons and concave and convex polygons. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Classifying Polygons”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Classifying Polygons” (HTML)
Instructions: Please click on the link above and complete questions 1–10 (“Lesson Exercises” on Pages 55 and 56 in the textbook). These questions will provide you with the opportunity to identify polygons and apply polygon properties. The solutions to these problems are located in the “Answers” section on page 56 of the textbook. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Classifying Polygons”

Unit 2: Parallel and Perpendicular Lines
Simply put, parallel lines are lines in a plane that do not intersect, while perpendicular lines are lines that intersect at a right angle (90°). Parallel and perpendicular lines are all around us. For example, railroad tracks, iron fencing, latticework, and kitchen tables all have parallel and/or perpendicular lines.
Time Advisory show close
Have you ever looked at a tile floor that has an intricate pattern of crisscrossing lines? The pattern has to be carefully replicated, following special rules. When parallel lines cross other lines, they create their own set of special rules, which may be used in making these patterns. In this unit, you will learn what happens when parallel lines cross other lines and how all the created angles relate to each other.
Learning Outcomes show close
 2.1 Lines

2.1.1 Parallel, Perpendicular, and Skew Lines
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Lines and Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Lines and Angles” (HTML)
Instructions: Please click on the link above and study the “Lines and Angles” section (Pages 117–122 of the textbook), stopping at “Angles and Transversals.” This section provides examples of parallel, perpendicular, and skew lines.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Identifying Parallel and Perpendicular Lines”
Link: Khan Academy’s “Identifying Parallel and Perpendicular Lines” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to learn how to identify parallel and perpendicular lines. Watch the presentation carefully two to three times to identify parallel and perpendicular lines.
Watching these lectures and pausing to take notes should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Lines and Angles”

2.1.2 Angles and Transversals
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles and Transversals”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles and Transversals” (HTML)
Instructions: Please click on the link above and study the “Angles and Transversals” section (Pages 122 and 123 in the textbook), stopping at “Review Questions” This section provides examples of different angles with a transversal line.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallel and Perpendicular Lines”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallel and Perpendicular Lines” (HTML)
Instructions: Please click on the link above and complete questions 1–10 (“Lesson Exercises” Pages 123–126 in the textbook). These questions will provide you with the opportunity to identify parallel, perpendicular, and skew lines as well as angles with transversals. The solutions to these problems are located in the “Answers” section on page 126 of the textbook.
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles and Transversals”
 2.2 Angles and Lines

2.2.1 Corresponding Angles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Corresponding Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Corresponding Angles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about corresponding angles. You do not need to watch the “James Sousa: Angles and Transversals,” “Properties of Parallel Lines,” and “Corresponding Angles Converse” videos. Watch the presentation carefully two or three times until you are able to understand problems with corresponding angles. Then, read the following sections: “Guidance” (including Corresponding Angles B video), “Vocabulary,” and “Guided Practice.” This section provides examples of corresponding angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the video, and taking notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Corresponding Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Corresponding Angles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to determine angles using corresponding angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Corresponding Angles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Corresponding Angles”

2.2.2 Alternate Interior Angles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Interior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Interior Angles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about alternate interior angles. You do not need to watch the “James Sousa: Angles and Transversals,” “Proof that Alternate Interior Angles are Congruent,” or “Proof of Alternate Interior Angles Converse” videos. Watch the presentation carefully two or three times until you are able to understand problems with alternate interior angles. Then, read the following sections: “Guidance” (including Alternate Interior Angles B video), “Vocabulary,” and “Guided Practice.” This section provides examples of corresponding angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the video, and taking notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Interior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Interior Angles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to determine angles using alternate interior angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Alternate Interior Angles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Interior Angles”

2.2.3 Alternate Exterior Angles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Exterior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Exterior Angles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about alternate exterior angles. You do not need to watch the “James Sousa: Angles and Transversals” and “Proof of Alternate Exterior Angles Converse” videos. Watch the presentation carefully two or three times until you are able to understand problems with alternate exterior angles. Then, read the following sections: “Guidance” (including Alternate Exterior Angles B video), “Vocabulary,” and “Guided Practice.” This section provides examples of alternate exterior angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Exterior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Exterior Angles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to determine angles using alternate exterior angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Alternate Exterior Angles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Alternate Exterior Angles”

2.2.4 Same Side Interior Angles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Same Side Interior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Same Side Interior Angles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about same side interior angles. You do not need to watch the “James Sousa: Angles and Transversals,” “Proof that Consecutive Interior Angles Are Supplementary,” and “Proof of Consecutive Interior Angles Converse” videos. Watch the presentation carefully two or three times until you are able to understand problems with same side interior angles. Then, read the following sections: “Guidance,” “Vocabulary” and “Guided Practice.” This section provides examples of same side interior angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Same Side Interior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Same Side Interior Angles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to determine angles using alternate exterior angles. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Same Side Interior Angles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Same Side Interior Angles”

2.2.5 Angle Game
 Lecture: Khan Academy’s “The Angle Game” and “Angle Game (Part 2)”
Link: Khan Academy’s “The Angle Game” (YouTube) and “Angle Game (Part 2)” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos to learn how to identify corresponding, alternate interior, alternate exterior, and same sideinterior angles. Watch the presentations carefully to understand the angle within each problem and how they are intertwined.
Watching these lectures and pausing to take notes should take approximately 1 hour and 15 minutes.
Terms of Use: These resources are licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. They are attributed to the Khan Academy.  Assessment: Khan Academy’s “Angles 1” and “Angles 2”
Link: Khan Academy’s “Angles 1” (HTML) and “Angles 2” (HTML)
Instructions: Please click on the links above, and complete the assessments that test your knowledge on corresponding, alternate interior, alternate exterior, and same side interior angles. You can review the concepts associated with these questions with the Khan videos in subsubunit 2.2.5. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.  Optional Activity: Optional Review Activity: Khan Academy's "Angles and Intersecting Lines"Link: Khan Academy’s “Angles and Intersecting Lines” (HTML)
Instructions: If you would like to review the previous lessons, please click on the link above and complete the exercise. You can review the concepts using the video contained within the exercise.
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “The Angle Game” and “Angle Game (Part 2)”

2.3 Distance Formula in the Coordinate Plane
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance Formula in the Coordinate Plane”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance Formula in the Coordinate Plane” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about find the distance between two points in the coordinate plane. You do not need to watch the “James Sousa: The Distance Formula” video. Watch the presentation carefully two or three times until you are able to understand problems finding the distance between two points. Then, read the following sections: “Guidance” (omitting Example C and the Distance Formula in the Coordinate Plane B video), “Vocabulary,” and “Guided Practice,” stopping at “Guide Practice” question 3. This section provides examples of find the distance between two points in the coordinate plane. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the video, and pausing to take notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance Formula in the Coordinate Plane”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance Formula in the Coordinate Plane” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–8 and 13. These exercises will provide you with the opportunity to find the distance between two points in the coordinate plane. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Distance Formula in the Coordinate Plane Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Distance Formula in the Coordinate Plane”

Unit 3: Triangles, Congruence, and Other Relationships
Making sure that objects are of equal size is important in life. Whether pieces of furniture, automobiles, or just pieces of a candy bar shared between siblings, we often have to make sure objects are the same size and shape.
Time Advisory show close
Have you ever had to prove something to a child? Sometimes, the best way to do that is to give the child a series of logical statements and then show how it all summarizes to one conclusion. In this unit, you will focus on showing that two triangles are identical. There are different methods to doing this, and the one you use will depend upon the information you have available to you. It is nothing more than following a series of logical statements and then showing how the statements draw a conclusion.
In this unit, you will also learn more about triangles and their various parts. Triangles, believe it or not, are used more often in life than you might think. Triangles are often used to estimate distances. The process of triangulation has been used for over two thousand years; with this technique, we can use two known locations and determine the distance to a location that we can see but cannot necessarily get to, like a boat out in a lake. Today, we use triangulation for navigating boats, surveying land, launching model rockets, and other activities.
We can also use triangles to map things out. For example, city planners often use the circumcenter of a triangle, which is a point in the middle that is equally distant from all three sides. They might use this to determine the location of a major parking garage, so that it is the same distance from three different companies, or they might want to make sure that a city monument is in the middle of a town plaza.
If you live in a house, triangles are right over your heads. Construction workers use the midsegment of a triangle to help strengthen roof trusses when they build. If the truss is not supported properly, it could collapse, leading to lots of problems for the poor homeowner.
Learning Outcomes show close

3.1 Triangle Classification
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Classification”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Classification” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about classifying triangles based on angles and sides. You do not need to watch the “James Sousa: Types of Triangles” video. Watch the presentation carefully two or three times until you are able to understand problems classifying triangles. Then, read the following sections: “Guidance” (omitting “Triangle Classification B” video), “Vocabulary,” and “Guided Practice.” This section provides examples of triangle classification. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Classification”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Classification” (HTML)
Instructions: Please click on the link above, select the “Exercises” tab, and complete the problems on classifying triangles. Determine the answer to the given problem, and select your response. Click on “Submit Answer” to see if the answer you chose is correct or incorrect. Select “Next” to move on to another question. You have completed the activity when you see “You have reached the maximum practice questions.” (Note: You can refresh the page if you would like additional practice problems and the questions will be different than the first set.) You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Triangle Types”
Link: Khan Academy’s “Triangle Types” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on vertical angles. You can review the concepts associated with these questions with the material in subunit 3.1. Select the correct answer choice for each problem. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Classification”
 3.2 Angle Properties of Triangles

3.2.1 Triangle Sum Theorem
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Sum Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Sum Theorem” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first two videos to learn about the sum of the interior angles of a triangle. You do not need to watch the “James Sousa: Proving the Triangle Sum Theorem” video. Watch the presentations carefully two or three times until you are able to understand why the angles of a triangle add up to 180 degrees. Then, read the following sections: “Guidance” (omitting the twocolumn proof of the Triangle Sum, but watching “Chapter 4 Triangle Sum Theorem B” video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding angles within a triangle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account.
Reading the material, watching the videos, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Sum Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Sum Theorem” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to find the missing angle(s) of triangles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Triangle Sum Theorem Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Sum Theorem”

3.2.2 Exterior Angle Theorem
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angle Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angle Theorem” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first two videos to learn about the exterior angles and the relationship with triangles. You do not need to watch the “James Sousa: Introduction to the Exterior Angles of a Triangle” and “Proof of the Exterior Angles Theorem” videos. Watch the presentations carefully two or three times until you are able to understand why the exterior angles add up to 360 degrees. Then, read the “Guidance” (omitting the twocolumn proof of the Exterior Angle Theorem, and “Chapter 4 Exterior Angles Theorem B” video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of how to find the missing interior and exterior angles of a triangle.
Reading the material, watching the videos, and pausing to take notes will take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angle Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angle Theorem” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–12. These exercises will provide you with the opportunity to find the missing angles of triangles as well as exterior angles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Exterior Angle Theorem Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angle Theorem”

3.2.3 Triangle Examples
Note: The material from subsubunits 1.4.5–1.4.7, 2.4, 3.2.1, and 3.2.2 is applicable to the problems within this subsubunit. If needed, please refer back to these sections of the course for review.
 Lecture: Khan Academy’s “Triangle Angle Example 2” and “Triangle Angle Example 3”
Link: Khan Academy’s “Triangle Angle Example 2” (YouTube) and “Triangle Angle Example 3” (YouTube)
Instructions: Please click on the links above, and take notes as you watch these videos to learn how to find missing angles of triangles by applying various properties. Watch the presentations carefully to understand how to find the missing angles of multiple triangles.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: These resources are licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. They are attributed to the Khan Academy.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Sums”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Sums” (HTML)
Instructions: Please click on the link above and complete exercises 1–13 (“Lesson Exercises pages 204 and 205 in the textbook). These exercises will provide you with the opportunity to find missing interior angles of a triangle and exterior angles. The solutions to these problems are located in the “Answers” section (on page 205 of the textbook).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Triangle Angles 1”
Link: Khan Academy’s “Triangle Angles 1” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on vertical angles. You can review the concepts associated with these questions with the material in subsubunits 3.2.1 and 3.2.2. Enter the value into the blank, and click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Triangle Angle Example 2” and “Triangle Angle Example 3”
 3.3 Triangle Congruence

3.3.1 Congruent Figures
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Figures”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Figures” (HTML)
Instructions: Please click on the link above and study the “Congruent Figures” section (Pages 206–212 in the textbook). This section provides discussions on defining and writing congruence statements in triangles, the third angle theorem, and congruence properties.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Figures”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Figures” (HTML)
Instructions: Please click on the link above and complete questionss 1–10 (“Lesson Exercises” Pages 212 and 213 in the textbook). These exercises will provide you with the opportunity to identify congruent figures and explain why certain triangles are congruent. The solutions to these problems are located in the “Answers” section (on page 213 of the textbook).
This activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Congruent Figures”

3.3.2 Congruent Triangles and SSS
 Lecture: Khan Academy’s “Congruence Triangles and SSS”
Link: Khan Academy’s “Congruence Triangles and SSS” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to review the properties of congruent triangles as well as the SideSideSide (SSS) Congruent Postulate for Triangles. Watch the presentation carefully two or three times to understand how to triangles are congruent by sidesideside.
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli’s Geometry: “Triangle Congruent Using SSS”
Link: CK12 Flexbook: Victor Cifarelli’s Geometry: “Triangle Congruent Using SSS” (HTML)
Instructions: Please click on the link above and study the “SSS Postulate of Triangle Congruence” section (Pages 217 and 218 in the textbook). This section provides the reasons why two triangles are congruent by using SSS.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli’s Geometry: “Triangle Congruent using SSS”
Link: CK12 Flexbook: Victor Cifarelli’s Geometry: “Triangle Congruent using SSS” (HTML)
Instructions: Please click on the link above and complete questions 1 and 810 (“Lesson Exercises” Pages 218 and 219 of the textbooks). These questions will provide you with the opportunity to identify congruent triangles by using SSS. The solutions to these problems are located in the “Answers” section (on page 219 of the textbook).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Congruence Triangles and SSS”

3.3.3 Other Triangle Congruent Postulates
 Lecture: Khan Academy’s “Other Triangle Congruence Postulates”
Link: Khan Academy’s “Other Triangle Congruence Postulates” (YouTube)
Instructions: Please click on the links above, and take notes as you watch this video to prove triangles are congruent by using the following postulates: SideAngleSide (SAS), AngleSideAngle (ASA), and AngleAngleSide (AAS). Watch the presentation carefully two or three times to understand how two triangles are congruent by these three congruence properties.
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Congruence Using ASA and AAS”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Congruence Using ASA and AAS” (HTML)
Instructions: Please click on the link above and study the “Triangle Congruence Using ASA and AAS” section (Pages 220–224 in the textbook), stopping at “Proving Triangles Congruent.” This section provides the reasons why two triangles are congruent by using ASA and AAS.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Congruence using ASA and AAS”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Congruence using ASA and AAS” (HTML)
Instructions: Please click on the link above and complete questions 1–9 (“Lesson Exercises” Pages 226 and 227 in the textbook. These questions will provide you with the opportunity to identify congruent triangles by using ASA and AAS. The solutions to these problems are located in the “Answers” section (on page 228 of the textbook).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: CK12 Flexbook: Victor Cifarelli’s Geometry: “Proof Using SAS and HL”
Link: CK12 Flexbook: Victor Cifarelli’s Geometry: “Proof Using SAS and HL” (HTML)
Instructions: Please click on the link above and study the “Proof Using SAS and HL” section (Pages 229 and 230 and 232–234 in the textbook), omitting “AAA and SSA Relationships” portion (Pages 230 and 231 in the textbook). This section provides you with the reasons why two triangles are congruent by using SAS and HL.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Congruence using ASA and AAS”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Congruence using ASA and AAS” (HTML)
Instructions: Please click on the link above and complete questions 1–9 (Pages 234 and 235 on the textbook). These questions will provide you with the opportunity to identify congruent triangles by using ASA and AAS. The solutions to these problems are located in the “Answers” section (page 236 in the textbook).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Other Triangle Congruence Postulates”

3.3.4 More on Why SSA Is Not a Postulate
 Lecture: Khan Academy’s “More on Why SSA Is Not a Postulate”
Link: Khan Academy’s “More on Why SSA Is Not a Postulate” (YouTube)
Instructions: Please click on the links above, and take notes as you watch this video to show why SideSideAngle cannot prove two triangles congruent. Watch the presentation carefully two or three times to understand how two triangles are not congruent by sidesideangle.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “AAA and SSA Relationships”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “AAA and SSA Relationships” (HTML)
Instructions: Please click on the link above and study the “AAA and SSA Relationships” (Pages 230 and 232 in the textbook), stopping at “Right Triangles”. This section provides the reasons why two triangles are not congruent by using AAA and SSA.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “More on Why SSA Is Not a Postulate”

3.3.5 Finding Congruent Triangles
 Lecture: Khan Academy’s “Finding Congruent Triangles”
Link: Khan Academy’s “Finding Congruent Triangles” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to determine which congruent triangle postulate proves two triangles to be congruent. Watch the presentation carefully two or three times to understand if two triangles are congruent by SSS, ASA, SAS, or AAS.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Assessment: Khan Academy’s “Congruent Triangles 1” and “Congruent Triangles 2”
Link: Khan Academy’s “Congruent Triangles 1” (HTML) and “Congruent Triangles 2” (HTML)
Instructions: Please click on the links above, and complete the assessments that test your knowledge on congruent triangles using the triangle congruence postulates. You can review the concepts associated with these questions with the Khan videos in subsubunits 3.3.2–3.3.5. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.  Optional Activity: Optional Review Activity: Khan Academy’s “Congruent Triangles” exercise.
Link: Khan Academy’s “Congruent Triangles” (HTML)
Instructions: If you would like to review the previous lessons, please click on the link above and complete the exercise. You can review the concepts using the video contained within the exercise.
Completing this activity should take approximately 15 minutes.
Terms of Use: These resources are licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Finding Congruent Triangles”

3.4 Isosceles Triangles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Isosceles Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Isosceles Triangles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first videos to learn about the isosceles triangles angles and their properties. You do not need to watch the “James Sousa: How to Construct an Isosceles Triangle” and “Proof of Isosceles Triangle Theorem” videos. Then, take notes as you watch the last video on “Using the Properties of Isosceles Triangle to Determine Values” (approximately 4 minutes) to learn about the isosceles triangles applications. Watch the presentations carefully two or three times until you are able to understand the properties of an isosceles triangle. Then, read the “Guidance” (omitting the twocolumn proof of the Base Angles Theorem and “Chapter 4 Isosceles Triangle B” video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of how to find the missing sides and angles of an isosceles triangle.
Reading the material, watching the video, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Another Isosceles Example Problem”
Link: Khan Academy’s “Another Isosceles Example Problem” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to determine the missing sides and angles of an isosceles triangle. Watch the presentation carefully two or three times to understand on how to write algebraic equations to find the missing angles and sides of an isosceles triangle.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Isosceles Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Isosceles Triangles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–9. These exercises will provide you with the opportunity to find the missing angles and sides of isosceles triangles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Isosceles Triangles Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Isosceles Triangles”

3.5 Equilateral Triangles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Equilateral Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Equilateral Triangles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first videos (approximately 4 minutes) to learn about the equilateral triangles angles and their properties. You do not need to watch the “James Sousa: How to Construct an Equilateral Triangle” and “Proof of Equilateral Triangle Theorem” videos. Then, take notes as you watch the last video on “Using the Properties of Equilateral Triangles” (approximately 4 minutes) to learn about the applications of equilateral triangles. Watch the presentations carefully two or three times until you are able to understand the properties of an isosceles triangle. Then, read the “Guidance” (omitting “Chapter 4 Equilateral Triangle B” video), “Vocabulary,” and “Guided Practice” (omitting Guided Practice #2) sections. This section provides examples of find the missing sides and angles of an equilateral triangle.
Reading the material, watching the video, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Equilateral Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Equilateral Triangles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to find the missing angles and sides of isosceles triangles. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Equilateral Triangles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Equilateral Triangles”

Unit 4: Triangle Relationships
In this unit, you will learn more about triangles and their various parts. Triangles, believe it or not, are used more often in life than you might think. Triangles are often used to estimate distances. The process of triangulation has been used for over two thousand years; with this technique, we can use two known locations and determine the distance to a location that we can see but cannot necessarily get to, like a boat out in a lake. Today, we use triangulation for navigating boats, surveying land, launching model rockets, and other activities.
Time Advisory show close
We can also use triangles to map things out. For example, city planners often use the circumcenter of a triangle, which is a point in the middle that is equally distant from all three sides. They might use this to determine the location of a major parking garage, so that it is the same distance from three different companies, or they might want to make sure that a city monument is in the middle of a town plaza.
If you live in a house, triangles are right over your heads. Construction workers use the midsegment of a triangle to help strengthen roof trusses when they build. If the truss is not supported properly, it could collapse, leading to lots of problems for the poor homeowner.
Learning Outcomes show close

4.1 Midsegment Theorem
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midsegments of a Triangle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midsegments of a Triangle” (HTML)
Instructions: Please click on the link above and study the “Midsegments of a Triangle” section (Pages 265–268 in the textbook), omitting “Proof of 1” and “Proof of 2” and stopping at “Review Questions.” This section provides examples and definitions of the midsegments of a triangle.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midsegments of a Triangle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midsegments of a Triangle” (HTML)
Instructions: Please click on the link above and complete questions 1–8 (Pages 268269 in the textbook). These questions will provide you with the opportunity to find the midsegments of a triangle. The solutions to these problems are located in the “Answers” section, starting on page 271 of the textbook.
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Midsegments of a Triangle”

4.2 Perpendicular Bisectors
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Perpendicular Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Perpendicular Bisectors” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about perpendicular bisectors and their properties. You do not need to watch the “James Sousa: Constructing Perpendicular Bisectors” and “Proof of Perpendicular Bisector Theorem” videos. Then, take notes as you watch the last video on “Determine Values Using Perpendicular Bisectors” to learn about the perpendicular bisector applications. Watch the presentation carefully two or three times until you are able to understand the properties of a perpendicular bisector in a triangle. Then, read the “Guidance” (omitting “Proof of the Perpendicular Bisector Theorem Converse,” and “Chapter 5 Perpendicular Bisectors B” video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of find the missing sides and angles of an equilateral triangle.
Reading the material, watching the video, and taking notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Perpendicular Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Perpendicular Bisectors” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1, 2, and 8–13. These exercises will provide you with the opportunity to apply the properties of perpendicular bisectors. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Perpendicular Bisectors Solutions” (PDF)
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Perpendicular Bisectors”

4.3 Angle Bisectors in Triangles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Bisectors in Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Bisectors in Triangles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about angle bisectors in triangles. You do not need to watch the “James Sousa: Introduction to Angle Bisectors,” “Proof of Angle Bisector Theorem,” and “Proof of the Angle Bisector Converse Theorem” videos. Then, take notes as you watch the last video on “Solving for Unknown Values Using Angle Bisectors” to learn about the angle bisector applications. Watch the presentation carefully two or three times until you are able to understand the properties of angle bisectors in a triangle. Then, read the “Guidance” (omitting “Proof of the Angle Bisector Theorem” and the “Chapter 5 Angle Bisectors B” video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of how to find the missing angles by using properties of an angle bisector.
Reading the material, watching the video, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Bisectors in Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Bisectors in Triangles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–8 and 10–13. These exercises will provide you with the opportunity to apply the properties of angle bisectors. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Angle Bisectors in Triangles Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angle Bisectors in Triangles”

4.4 Medians
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Medians in Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Medians in Triangles” (HTML)
Instructions: Please click on the link above and study the “Medians in Triangles” section (Pages 296 and 297 in the textbook), stopping at “Napoleon’s Theorem.” This section provides examples and a definition of the median in a triangle.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Median Centroid Right Triangle Example”
Link: Khan Academy’s “Median Centroid Right Triangle Example” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to determine the length of the median of a triangle. Watch the presentation carefully two or three times to understand the centroid and properties of a median.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Medians in Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Medians in Triangles” (HTML)
Instructions: Please click on the link above and complete questions 2–5 and 7 (Pages 300–302 in the textbook). These questions will provide you with the opportunity to find the medians and the centroid of a triangle. The solutions to these problems are located in the “Answers” section (page 302 in the textbook).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Medians in Triangles”

4.5 Altitudes
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Altitudes in Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Altitudes in Triangles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about altitudes in triangles. Read the overview until you are able to understand altitudes within triangles. This reading also provides examples of how to find the altitude of a triangle. Then, complete Review Questions 18 and check your answers.
Reading the material, pausing to take notes, and completing the review questions should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Optional Activity: Optional Review Activity: Khan Academy’s “Special Properties and Parts of Triangles”
Link: Khan Academy’s “Special Properties and Parts of Triangles” (HTML)
Instructions: If you would like to review the previous lessons, please click on the link above and complete the exercise. You can review the concepts using the video contained within the exercise.
Completing this activity should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Altitudes in Triangles”
 4.6 Triangle Inequalities

4.6.1 Triangle Inequality Theorem
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Inequality Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Inequality Theorem” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the triangle inequality theorem. Watch the presentation carefully two or three times until you are able to understand and apply the triangle inequality theorem. Then, read the “Guidance” (omitting the “Chapter 5 Triangle Inequality Theorem B” video), “Vocabulary,” and “Guided Practice” sections. This section provides applications of the triangle inequality theorem, which states that any side of a triangle must be equal to or less than the sum of the other two sides in order to form the triangle.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Inequality Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Inequality Theorem” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–16. These exercises will provide you with the opportunity to apply the triangle inequality theorem. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Triangle Inequality Theorem Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Triangle Inequality Theorem”

4.6.2 Inequalities in Two Triangles
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inequalities in Two Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inequalities in Two Triangles” (HTML)
Instructions: Please click on the link above and study the “Inequalities in Two Triangles”, section (Pages 320–323 in the textbook), omitting the proofs of the SSS Inequality Theorem and SAS Inequality Theorem and stopping at “Review Questions.” This section provides examples and definitions of triangle inequality theorems.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inequalities in Two Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inequalities in Two Triangles” (HTML)
Instructions: Please click on the link above and complete questions 1–10, (Pages 323–326 of the textbook). These questions will provide you with the opportunity to apply the inequality triangle theorems. The solutions to these problems are located in the “Answers” section (starting on page 326 in the textbook).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Triangle Inequality Theorem”
Link: Khan Academy’s “Triangle Inequality Theorem” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on the triangle inequality theorem. You can review the concepts associated with these questions with the content from subsubunit 4.6.1 and 4.6.2. Determine the value for the problem and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inequalities in Two Triangles”

Unit 5: Polygons and Quadrilaterals
Polygons are everywhere around us. If you see a shape that has no curves, then it is a polygon. As a child, you probably learned the names of many common polygons. In this unit, you will focus on quadrilaterals, which are polygons with four sides. They each have their own set of characteristics and share some characteristics with other quadrilaterals. You will learn to recognize these characteristics and to use them to help you answer questions about quadrilaterals.
Time Advisory show close
Learning Outcomes show close

5.1 Sum of Interior Angles of a Polygon
 Lecture: Khan Academy’s “Sum of Interior Angles of a Polygon”
Link: Khan Academy’s “Sum of Interior Angles of a Polygon” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to determine how to find the sum of the interior angles of a polygon. Watch the presentation carefully two or three times to understand how to determine the sum of the interior angles of a polygon.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Interior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Interior Angles” (HTML)
Instructions: Please click on the link above and study the “Interior Angles” section (Pages 331–333 in the textbook), stopping at “Review Questions.” This section provides examples of how to find the sum of the interior angles of a polygon.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Interior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Interior Angles” (HTML)
Instructions: Please click on the link above and complete questions 1–10 (“Lesson Exercises” Pages 334 and 335 in the textbook). These questions will provide you with the opportunity to apply the sum of interior angles of a polygon. The solutions to these problems are located in the “Answers” section (starting on page 335 in the textbook).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Sum of Interior Angles of a Polygon”

5.2 Sum of Exterior Angles of a Convex Polygon
 Lecture: Khan Academy’s “Sum of Exterior Angles of a Convex Polygon”
Link: Khan Academy’s “Sum of Exterior Angles of a Convex Polygon” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to determine how to find the sum of the exterior angles of a polygon. Watch the presentation carefully two or three times to understand how to determine the sum of the exterior angles of a polygon.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angles” (HTML)
Instructions: Please click on the link above and study the “Exterior Angles” section (Pages 336–341 in the textbook), stopping at “Review Questions” (Exercise Lessons in the Textbook). This section provides examples of how to find the sum of the exterior angles of a polygon.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Exterior Angles” (HTML)
Instructions: Please click on the link above and complete questions 1–8, (“Lesson Exercises” Pages 341 and 342 in the textbook). These questions will provide you with the opportunity to apply the sum of exterior angles of a polygon. The solutions to these problems are located in the “Answers” section (starting on page 343 in the textbook).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Angles of a Polygon”
Link: Khan Academy’s “Angles of a Polygon” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on the interior and exterior angles of a polygon. You can review the concepts associated with these questions with the content from subunit 5.1 and 5.2. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Sum of Exterior Angles of a Convex Polygon”

5.3 Parallelograms
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelograms”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelograms” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the properties of a parallelogram. Watch the presentations carefully two or three times until you are able to understand and apply the properties of a parallelogram. Then, read the “Guidance” (omitting “Proof of Opposite Theorems”), “Vocabulary,” and “Guided Practice” sections. This section provides examples of applying parallelogram properties.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelograms”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelograms” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–23 and 26–29. These exercises will provide you with the opportunity to apply the parallelogram properties. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Parallelograms Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelograms”

5.4 Parallelogram Classification
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelogram Classification”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelogram Classification” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about classifying other parallelogram and their properties. Watch the presentations carefully two or three times until you are able to understand these properties of other parallelograms. Then, read the “Guidance” (omitting “Example C”), “Vocabulary,” and “Guided Practice” sections. This section provides examples of applying parallelogram properties.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelogram Classification”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelogram Classification” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–19. These exercises will provide you with the opportunity to apply the parallelogram properties. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Parallelogram Classification Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parallelogram Classification”

5.5 Trapezoids
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trapezoids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trapezoids” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about trapezoids and their properties. Watch the presentations carefully two or three times until you are able to understand these properties of trapezoids. Then, read the “Guidance” (omitting “Example B”), “Vocabulary,” and “Guided Practice” sections. This section provides examples of applying trapezoid properties.
Reading the material, watching the videos, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trapezoids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trapezoids” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–10 as well as 14 and 15. These exercises will provide you with the opportunity to apply the parallelogram properties. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Trapezoids Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trapezoids”

5.6 Kites
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Kites”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Kites” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about kites and their properties. Watch the presentations carefully two or three times until you are able to understand these properties of kites. Then, read the “Guidance” (omitting “Proof”), “Vocabulary,” and “Guided Practice” sections. This section provides examples of applying kite properties.
Reading the material, watching the videos, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Kites”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Kites” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–11, as well as 14 and 15. These exercises will provide you with the opportunity to apply the kite properties. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Kites Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Kites”
 5.7 Quadrilateral Classification

5.7.1 Coordinate Geometry
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Quadrilateral Classification”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Quadrilateral Classification” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about classifying quadrilaterals using coordinate geometry. Watch the presentations carefully two or three times until you are able to understand these properties of quadrilaterals. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of applying these properties to determine the quadrilateral.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Quadrilateral Classification”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Quadrilateral Classification” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to apply the properties of quadrilaterals. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Quadrilateral Classification Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Quadrilateral Classification”

5.7.2 Quadrilateral Overview
 Lecture: Khan Academy’s “Quadrilateral Overview” and “Quadrilateral Properties”
Link: Khan Academy’s “Quadrilateral Overview” (YouTube) and “Quadrilateral Properties” (YouTube)
Instructions: Please click on the link above and take notes as you watch these videos to recognize various special parallelograms. Watch these presentations carefully two or three times to understand how to determine various parallelograms.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: These resources are licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. They are attributed to the Khan Academy.  Optional Activity: Optional Review Activity: Khan Academy’s “Quadrilateral types"
Link: Khan Academy’s “Quadrilaterals” (HTML)
Instructions: If you would like to review this lesson, please click on the link above and complete the exercise. You can review the concepts using the video contained within the exercise.
Completing this activity should take approximately 15 minutes.
Terms of Use: These resources are licensed under a Creative Commons AttributionShareAlike License 3.0. They are attributed to the Khan Academy.  Assessment: Khan Academy’s “Quadrilateral Types” and “Quadrilateral and Polygons Challenge”
Link: Khan Academy’s “Quadrilateral Types” (HTML) and “Quadrilateral and Polygons Challenge” (HTML)
Instructions: Please click on the link above and complete the assessments that test your knowledge on the types of polygons. You can review the concepts associated with these questions with the content from subsubunit 5.7.2. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: These resources are licensed under a Creative Commons AttributionShareAlike License 3.0. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Quadrilateral Overview” and “Quadrilateral Properties”

Unit 6: Similarity
In this unit, you will review ratios and proportions, and you will learn how they connect to similarity. In the real world, you may see an item and think that it is similar to something else, whether it is because of the design, the size, or some other factors. In Geometry, however, similarity has very strict rules attached to it. You will learn to apply these rules to determine if two shapes, especially triangles, are similar.
Time Advisory show close
Learning Outcomes show close

6.1 Similar Polygons
 Lecture: Khan Academy’s “Similar Triangle Basics”
Link: Khan Academy’s “Similar Triangle Basics” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand properties of similar triangles. Watch this presentation carefully two or three times to understand what the relationship is between sides and angles of similar figures.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Optional Activity: Optional Review Activity: Khan Academy’s “Similarity” exercise
Link: Khan Academy’s “Similarity” (HTML)
Instructions: If you would like to review this lesson, please click on the link above and complete the exercise. You can review the concepts using the video contained within the exercise.
Completing this activity should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similar Polygons and Scale Factors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similar Polygons and Scale Factors” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about similar polygons and scale factor. Watch the presentations carefully two or three times until you are able to understand the relationship between angles and sides in similar polygons. Then, read the “Guidance” (omitting the “Similar Polygons and Scale Factors B” video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of applying these properties to similar figures.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similar Polygons and Scale Factors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similar Polygons and Scale Factors” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–29. These exercises will provide you with the opportunity to apply the properties of similar figures. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Similar Polygons and Scale Factors Solutions” (PDF).
Completing this activity should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Similar Triangles 1” and “Similar Triangles 2”
Link: Khan Academy’s “Similar Triangles 1” (HTML) and “Similar Triangles 2” (HTML)
Instructions: Please click on the link above and complete the assessments that test your knowledge on similar triangles and their properties. You can review the concepts associated with these questions with the content from subunit 6.1. Determine the value for the problem and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: These resources are licensed under a Creative Commons AttributionShareAlike License 3.0. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Similar Triangle Basics”

6.2 Similarity Postulates
 Lecture: Khan Academy’s “Similarity Postulates”
Link: Khan Academy’s “Similarity Postulates” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand postulates of similar triangles. Watch this presentation carefully two or three times to understand how to determine similarity postulates of similar triangles.
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Similarity Postulates”

6.2.1 AngleAngle (AA) Similarity and Indirect Measurement
 Lecture: Khan Academy’s “Similarity Triangle Example Problems”
Link: Khan Academy’s “Similarity Triangle Example Problems” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand sample problems of similar triangles. Watch this presentation carefully two or three times to understand how to find missing sides and angles of similar triangles. This lecture also applies to the topic outlined in subsubunit 6.2.2.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by AA”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by AA” (HTML)
Instructions: Please click on the link above and study the “Similarity by AA” section (Pages 425–428 in the textbook), stopping at “Review Questions”. This section provides examples of how to prove triangles are similar by AA and how to indirectly measure items.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by AA”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by AA” (HTML)
Instructions: Please click on the link above and complete questions 1–12, (“Lesson Exercises” Pages 428–430 in the textbook). These exercises will provide you with the opportunity to apply AA similarity and indirect measurement. The solutions to these problems are located in the “Answers” section (starting on page 430 of the textbook).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Similarity Triangle Example Problems”

6.2.2 SideSideSide (SSS) Similarity and SideAngleSide (SAS) Similarity
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by SSS and SAS”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by SSS and SAS” (HTML)
Instructions: Please click on the link above and study the “Similarity by SSS and SAS” section, (Pages 431–434 in the textbook), stopping at “Review Questions.” This section provides examples of how to prove triangles are similar by SSS and SAS and how to find missing parts of similar triangles.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by SSS and SAS”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by SSS and SAS” (HTML)
Instructions: Please click on the link above and complete questions 1–11, (“Lesson Exercises” Pages 434 and 435 in the textbook). These questions will provide you with the opportunity to apply SSS and SAS similarity. The solutions to these problems are located in the “Answers” section (starting on page 435 of the textbook).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Similarity by SSS and SAS”

6.3 Triangle Proportionality and Parallel Lines and Transversals
 Lecture: Khan Academy’s “Similarity Example Problems”
Link: Khan Academy’s “Similarity Example Problems” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand sample problems of similar triangles. Watch this presentation carefully two or three times to understand how to find missing sides and angles of similar triangles.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportionality Relationships”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportionality Relationships” (HTML)
Instructions: Please click on the link above and study the “Proportionality Relationships” section, (Pages 436–443 in the textbook, omitting the proof on page 438), and stopping at “Review Questions.” This section provides examples of how to find missing parts of similar triangles in other forms.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportionality Relationships”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportionality Relationships” (HTML)
Instructions: Please click on the link above and complete questions 1–9, (“Lesson Exercises” Pages 443 and 444 of the textbook). These questions will provide you with the opportunity to apply proportionality relationships. The solutions to these problems are located in the “Answers” section (starting on page 444 of the textbook).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Solving Similar Triangles 1” and “Solving Similar Triangles 2”
Link: Khan Academy’s “Solving Similar Triangles 1” (HTML) and “Solving Similar Triangles 2” (HTML)
Instructions: Please click on the links above, and complete the assessments that test your knowledge on finding missing sides and angles of similar triangles. You can review the concepts associated with these questions with the content from subunit 6.2 and 6.3. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Similarity Example Problems”

6.4 Proportions with Angle Bisectors
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportions with Angle Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportions with Angle Bisectors” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about proportions with angle bisectors in triangles. You do not need to watch the “James Sousa: Triangle Angle Bisector Theorem” video. Then, take notes as you watch the last video on “Triangle Angle Bisector Theorem” to learn about the angle bisector applications. Watch the presentation carefully two or three times until you are able to understand the properties of the triangle angle bisector theorem. Then, read the “Guidance” (omitting “Chapter 7 Proportions with Angle Bisectors B” video), “Vocabulary,” and “Guided Practice” sections. This section provides examples of how to find the missing angles using properties of an angle bisector.
Reading the material, watching the videos, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportions with Angle Bisectors”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportions with Angle Bisectors” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–4 and 6–19. These exercises will provide you with the opportunity to apply the properties of the triangle angle bisectors theorem. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Proportions with Angle Bisectors Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Proportions with Angle Bisectors”

Unit 7: Right Triangle Trigonometry
In this unit, you will learn the basics of trigonometry. Trigonometry is used for several different measuring techniques. You can determine the height of a building, for example, if you know how far away you are standing and at what angle your eyes form when looking up to its top. In previous centuries, mariners could use trigonometry to help them set their course, using the heavens as a guide.
Time Advisory show close
Learning Outcomes show close

7.1 Pythagorean Theorem
 Lecture: Khan Academy’s “Pythagorean Theorem”
Link: Khan Academy’s “Pythagorean Theorem” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand the Pythagorean Theorem. Watch this presentation carefully two or three times to understand how to find missing sides by using this formula.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pythagorean Theorem and Pythagorean Triples”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pythagorean Theorem and Pythagorean Triples” (HTML and YouTube)
Instructions: Please click on the link above and take notes on the section. You do not need to watch the “James Sousa: Pythagorean Theorem video. Read the “Guidance” (omitting Another Proof of the Pythagorean Theorem), “Vocabulary,” and “Guided Practice” sections. This section provides examples of applying the Pythagorean Theorem.
Reading these sections and taking notes should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pythagorean Theorem and Pythagorean Triples”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pythagorean Theorem and Pythagorean Triples” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–16. These exercises will provide you with the opportunity to apply the Pythagorean Theorem. You may also access the material in PDF, Mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Pythagorean Theorem and Pythagorean Triples Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Converse of the Pythagorean Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Converse of the Pythagorean Theorem” (HTML)
Instructions: Please click on the link above and study the “Converse of the Pythagorean Theorem” section (Pages 469–474 in the textbook), stopping at “Review Questions.” This section provides examples of how to identify triangle types from the Pythagorean Theorem.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Converse of the Pythagorean Theorem”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Converse of the Pythagorean Theorem” (HTML)
Instructions: Please click on the link above and complete questions 1–9 (“Lesson Exercises” Pages 474 and 475 in the textbook). These questions will provide you with the opportunity to determine triangles by using the Pythagorean Theorem. The solutions to these problems are located in the “Answers” section (starting on page 475 of the textbook).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Pythagorean Theorem”
Link: Khan Academy’s “Pythagorean Theorem” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on finding missing sides using the Pythagorean Theorem. You can review the concepts associated with these questions with the Khan videos from subunit 7.1. Determine the value for the problem and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Pythagorean Theorem”

7.2 454590 Triangles
 Lecture: Khan Academy’s “454590 Triangles”
Link: Khan Academy’s “454590 Triangles” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand the relationship between the angles and sides of a 454590 triangle. Watch this presentation carefully two or three times to understand how to find missing sides using this triangle.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “454590Right Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “454590Right Triangles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about 454590 right triangles. You do not need to watch the “James Sousa: Trigonometric Function Values of Special Angles” and “Solving Special Right Triangles” videos. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of problems using 454590 triangles.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “454590 Right Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “454590 Right Triangles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to apply the relationship between the sides of a 454590 right triangle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “454590 Right Triangles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “454590 Triangles”

7.3 306090 Right Triangles
 Lecture: Khan Academy’s “306090 Triangles II”
Link: Khan Academy’s “306090 Triangles II” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand the relationship between the angles and sides of a 306090 triangle. Watch this presentation carefully two or three times to understand how to find missing sides by applying the properties of this triangle.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “306090Right Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “306090Right Triangles” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about 306090 right triangles. You do not need to watch the “James Sousa: Trigonometric Function Values of Special Angles” and “Solving Special Right Triangles” videos. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of problems using 306090 triangles.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “306090Right Triangles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “306090Right Triangles” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–13. These exercises will provide you with the opportunity to apply the relationship between the sides of a 306090 right triangle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “306090 Right Triangles Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Special Right Triangles”
Link: Khan Academy’s “Special Right Triangles” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on finding the missing sides of special right triangles. You can review the concepts associated with these questions with the Khan videos from subunits 7.2 and 7.3. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “306090 Triangles II”

7.4 Sine, Cosine, and Tangent
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Sine, Cosine, and Tangent”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Sine, Cosine, and Tangent” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about trigonometric ratios. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of problems using these trigonometric ratios in right triangles.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Sine, Cosine, and Tangent”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Sine, Cosine, and Tangent” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–16. These exercises will provide you with the opportunity to apply the relationships of various trigonometric ratios. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Sine, Cosine, and Tangent Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Trigonometry 0.5”
Link: Khan Academy’s “Trigonometry 0.5” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on basic trigonometric ratios. You can review the concepts associated with these questions from subunit 7.4. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Sine, Cosine, and Tangent”

7.5 Trigonometric Ratios with a Calculator
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trigonometric Ratios with a Calculator”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trigonometric Ratios with a Calculator” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about finding trigonometric ratios with a calculator. You do not need to watch the “James Sousa: Determining Trigonometric Function Values on the Calculator” video. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of solving problems by using a calculator to find the trigonometric ratios.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trigonometric Ratios with a Calculator”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trigonometric Ratios with a Calculator” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–12. These exercises will provide you with the opportunity to use a calculator to find various trigonometric ratios. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Trigonometric Ratios with a Calculator Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Trigonometric Ratios with a Calculator”

Unit 8: Circles
Circles are everywhere you look, for example, tires, pools, fans, and watches. You can probably think of several more items that are circular. In this unit, you will learn about circles and arcs, which are slices of the edge of a circle.
Time Advisory show close
Believe it or not, arcs are used a lot in real life. The feet of a rocking chair are arcs; the crust on a slice of pizza is an arc. Anything that looks like an incomplete circle is an arc. How are these arcs made? What kinds are there? How can we measure them? These are questions that you will explore in this unit.
Learning Outcomes show close

8.1 Language and Notation of a Circle
 Lecture: Khan Academy’s “Language and Notation of a Circle”
Link: Khan Academy’s “Language and Notation of a Circle” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand the language and notation associated with a circle. Watch this presentation carefully two or three times to understand how to identify parts of a circle.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parts of a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parts of a Circle” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about finding trigonometric ratios with a calculator. You do not need to watch the “James Sousa: Introduction to Circles” video. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of recognizing various parts of a circle.
Reading the material, watching the video, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parts of a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Parts of a Circle” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to recognize various parts of a circle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Parts of a Circle Measurement Solutions” (PDF).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Language and Notation of a Circle”

8.2 Tangent Lines
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Tangent Lines”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Tangent Lines” (HTML)
Instructions: Please click on the link above and study the “Tangent Lines” section (Pages 536–543 in the textbook) omitting the “Proof “ (Pages 537, 538, 540, and 541), stopping at “Proof” on page 543. This section provides examples of how to identify tangent lines and its properties.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Tangent Lines”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Tangent Lines” (HTML)
Instructions: Please click on the link above and complete questions 1–8 (“Lesson Exercises” Pages 545–550 in the textbook). These questions will provide you with the opportunity to apply properties of tangent lines and circles. The solutions to these problems are located in the “Answers” section (starting on page 550 of the textbook).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Tangent Lines”

8.3 Arcs in Circles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arcs in a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arcs in a Circle” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the first video to learn about arcs in a circle. You do not need to watch the “Central Angles” video. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of recognizing arcs of a circle and applying various properties.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arcs in a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arcs in a Circle” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–24. These exercises will provide you with the opportunity to recognize various parts of a circle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Arcs in a Circle Solutions” (PDF).
This activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arcs in a Circle”

8.4 Chords in Circles
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Chords in a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Chords in a Circle” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about chords in a circle. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” (omitting Guided Practice Problem #3) sections. This section provides examples of recognizing chords of a circle and applying various properties.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Chords in a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Chords in a Circle” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15 and 18–20. These exercises will provide you with the opportunity to apply theorems related to chords. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Chords in a Circle Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Chords in a Circle”

8.5 Inscribed Angles
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inscribed Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inscribed Angles” (HTML)
Instructions: Please click on the link above and study the “Inscribed Angles” section (Pages 582–585 in the textbook), omitting the “Proof” (Pages 582 and 583) and stopping at “Review Questions.” This section provides examples of inscribed angles in circles and their properties.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inscribed Angles”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inscribed Angles” (HTML)
Instructions: Please click on the link above and complete questions 1–3, 8, and 9 (“Lesson Exercises” Pages 585–588 of the textbook. These exercises will provide you with the opportunity to apply properties of inscribed angles. The solutions to these problems are located in the “Answers” section (starting on page 588 of the textbook).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Inscribed Angles”

8.6 Angles of Chords, Secants, and Tangents
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles of Chords, Secants, and Tangents”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles of Chords, Secants, and Tangents” (HTML)
Instructions: Please click on the link above and study the “Angles of Chords, Secants, and Tangents” section (Pages 590–595 in the textbook), omitting the “Proof” (Pages 590–594), and stopping at “Review Questions.” This section provides examples on angles of chords, secants, and tangents.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles of Chords, Secants, and Tangents”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles of Chords, Secants, and Tangents” (HTML)
Instructions: Please click on the link above and complete questions 1–4 (“Lesson Exercises”) 595–600 of the textbook. These exercises will provide you with the opportunity to apply properties of angles of chords, secants, and tangents. The solutions to these problems are located in the “Answers” section (starting on page 601 of the textbook).
Completing this activity should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles of Chords, Secants, and Tangents”

8.7 Segments of Chords, Secants, and Tangents
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Segments of Chords, Secants, and Tangents”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Segments of Chords, Secants, and Tangents” (HTML)
Instructions: Please click on the link above and study the “Segments of Chords, Secants, and Tangents” section (Pages 602–607 in the textbook), omitting the “Proof” (Pages 603 and 604) and stopping at “Review Questions.” This section provides examples on segments of chords, secants, and tangents.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles of Chords, Secants, and Tangents”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Angles of Chords, Secants, and Tangents” (HTML)
Instructions: Please click on the link above and complete questions 1–4 (“Lesson Exercises” Pages 607–613 in the textbook). These questions will provide you with the opportunity to apply properties of segments of chords, secants, and tangents. The solutions to these problems are located in the “Answers” section (starting on page 613 of the textbook).
Completing this activity should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Segments of Chords, Secants, and Tangents”

Unit 9: Perimeter and Area
Two of the most common applications of Geometry are area and perimeter. Owning a home gives you plenty of opportunities to use these concepts. Thinking of buying a cordless electric lawnmower? The manufacturer will give you an estimate of the mower’s battery life using square feet. If your yard is extremely large and your mower’s battery life is not long enough, it might take you multiple sessions to get it all mowed. Are you buying new carpeting for your home? It is sold in square feet or square yards. You definitely do not want to buy too much carpeting or too little carpeting. You are not just going to eyeball it and make a guess. You will want to measure everything carefully, and then order a bit more, giving yourself some leeway.
Time Advisory show close
Like area, perimeter is often used in home ownership. If you install fencing around your yard, you are going to calculate the perimeter before you buy the fencing. If you are forced to run wiring around the walls of a room, it is vital that you know how much wiring you will need.
Learning Outcomes show close

9.1 Perimeter and Area Basics
 Lecture: Khan Academy’s “Perimeter and Area Basics”
Link: Khan Academy’s “Perimeter and Area Basics” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand the basics of area and perimeter. Watch this presentation carefully two or three times to understand how to determine difference of the area and perimeter.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Perimeter and Area Basics”

9.2 Area of Triangles
 Lecture: Khan Academy’s “Area and Perimeter”
Link: Khan Academy’s “Area and Perimeter” (YouTube)
Instructions: Please click on the link above and start the video at the 6:40 mark. Take notes as you watch this video to understand the basics of finding the area and perimeter of a triangle. Watch this presentation carefully two or three times to understand how to find the area and perimeter of a triangle.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Triangle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Triangle” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the video to learn about area and perimeter of a triangle. You may omit watching the “Area of Triangles” video. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the perimeter and area of various triangles.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Triangle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Triangle” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of a triangle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Area and Perimeter of a Triangle Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Area of Triangles”
Link: Khan Academy’s “Area of Triangles” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on the area of triangles. You can review the concepts associated with these questions from subunit 9.2. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Area and Perimeter”

9.3 Area and Perimeter of Rectangles and Squares
 Lecture: Khan Academy’s “Area and Perimeter”
Link: Khan Academy’s “Area and Perimeter” (YouTube)
Instructions: Please click on the link above and watch the video up until the 6:40 mark. Take notes as you watch this video to understand the basics of finding the area and perimeter of a rectangle and a square. Watch this presentation carefully two or three times to understand how to find the area and perimeter of a rectangle and a square.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Rectangle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Rectangle” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the video to learn about area and perimeter of a rectangle. You may omit watching the “Math Made Easy: Finding the Area of Rectangles” video. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the perimeter and area of a various rectangle.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Rectangle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of a Rectangle” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of a rectangle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Area and Perimeter of a Rectangle Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Perimeter of Squares and Rectangles” and “Area of Squares and Rectangles”
Link: Khan Academy’s “Perimeter of Squares and Rectangles” (HTML) and “Area of Squares and Rectangles” (HTML)
Instructions: Please click on the links above, and complete the assessments that test your knowledge on the area and perimeter of squares and rectangles. You can review the concepts associated with these questions from subunit 9.3. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 15 minutes.
Terms of Use: These resources are licensed under a Creative Commons AttributionShareAlike License 3.0. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Area and Perimeter”

9.4 Area of a Parallelogram
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Parallelogram”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Parallelogram” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the video to learn about the area of a parallelogram. You may omit watching the “Area of Parallelograms” video. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the area of various parallelograms.
Reading the material, watching the video, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Parallelogram”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Parallelogram” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–16. These exercises will provide you with the opportunity to apply the formulas for the area of a parallelogram. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Area of a Parallelogram Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Parallelogram”

9.5 Area and Perimeter of Trapezoids
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Trapezoids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Trapezoids” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about area and perimeter of a trapezoid. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the area and perimeter of various trapezoids.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Trapezoids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Trapezoids” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–16 and 18. These exercises will provide you with the opportunity to apply the formulas for the area and perimeter of a trapezoid. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Area and Perimeter of a Trapezoids Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Trapezoids”

9.6 Area and Perimeter of Rhombuses and Kites
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Rhombuses and Kites”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Rhombuses and Kites” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the area and perimeter of a rhombus and a kite. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the area and perimeter of various rhombuses and kites.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Rhombuses and Kites”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Rhombuses and Kites” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 4–21. These exercises will provide you with the opportunity to apply the formulas for area and perimeter of a rhombus and a kite. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Area and Perimeter of Rhombuses and Kites Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Area of Trapezoids, Rhombi, and Kites”
Link: Khan Academy’s “Area of Trapezoids, Rhombi, and Kites” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on the area of trapezoids, rhombi, and kites. You can review the concepts associated with these questions from subunits 9.5 and 9.6. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area and Perimeter of Rhombuses and Kites”

9.7 Area of Similar Polygons
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Areas of Similar Polygons”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Areas of Similar Polygons” (HTML)
Instructions: Please click on the link above and study the “Areas of Similar Polygons” section (Pages 630–636 in the textbook), stopping at “Review Questions.” This section provides examples on area of similar polygons.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Areas of Similar Polygons”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Areas of Similar Polygons” (HTML)
Instructions: Please click on the link above and complete questions 1–13 (“Lesson Exercises” Pages 636 and 637 in the textbook). These questions will provide you with the opportunity to apply properties of areas of similar polygon. The solutions to these problems are located in the “Answers” section (starting on page 637 of the textbook).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Areas of Similar Polygons”

9.8 Circumference
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Circumference”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Circumference” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the circumference of a circle. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the circumference of a circle.
Reading the material, watching the videos, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Circumference”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Circumference” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–18. These exercises will provide you with the opportunity to apply the formulas for circumference of a circle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Circumference Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Circumference”

9.9 Arc Length
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arc Length”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arc Length” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the arc length of a circle. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the arc length of a circle.
Reading the material, watching the videos, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arc Length”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arc Length” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to apply the formulas for arc length of a circle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Arc Length Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Arc Length”

9.10 Area of a Circle
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Circle” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the area of a circle. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the area of a circle.
Reading the material, watching the videos, and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Circle”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Circle” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to apply the formulas for area of a circle. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Area of a Circle Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Area of a Circle”
Link: Khan Academy’s “Area of a Circle” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on the area of circles. You can review the concepts associated with these questions from subunit 9.10. Determine the value for the problem, and enter your answer in the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of a Circle”

9.11 Area of Composite Shapes
 Lecture: Khan Academy’s “Perimeter and Area of a NonStandard Polygon”
Link: Khan Academy’s “Perimeter and Area of a NonStandard Polygon” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to understand the basics of finding the area of composite shapes. Watch this presentation carefully two or three times to understand how to find the area of composite figures.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of Composite Shapes”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of Composite Shapes” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the area of composite shapes. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the area of composite shapes.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of Composite Shapes”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Area of Composite Shapes” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–15. These exercises will provide you with the opportunity to apply the formulas for area to find the areas of composite figures. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Area of Composite Shapes Solutions” (PDF).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Perimeter and Area of a NonStandard Polygon”

Unit 10: Surface Area and Volume
Finding the amount of space inside of an object is important, and something you will do in your everyday life. If you try to fill a box with DVDs, to fill up a sandbox, or to fill a pool with water, you will use concept of volume. There are more shapes than just simple boxes, so you will learn to find the amount of space inside different types of threedimensional objects.
Time Advisory show close
Finding the amount of space on the outside of an object is also something you will do in your everyday life. If you decide to paint your house, you need to know how much space is going to be painted; buying too much paint would be a waste of money, and buying too little paint would be a nuisance. A few minutes of calculating can ensure that you get the amount of paint you need.
Learning Outcomes show close

10.1 Polyhedrons
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “The Polyhedron”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “The Polyhedron” (HTML)
Instructions: Please click on the link above and study the “The Polyhedron” section (Pages 665–671 in the textbook), stopping at “Review Questions.” This reading defines various terms associated with polyhedron.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “The Polyhedron”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “The Polyhedron” (HTML)
Instructions: Please click on the link above and complete questions 1–10 (“Lesson Exercises” Pages 671–673 of the textbook). These questions will provide you with the opportunity to apply properties of threedimensional figures. The solutions to these problems are located in the “Answers” section (starting on page 673 of the textbook).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “The Polyhedron”

10.2 Representing Solids
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Representing Solids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Representing Solids” (HTML)
Instructions: Please click on the link above and study the “The Polyhedron” section (Pages 674–681 in the textbook), stopping at “Review questions.” This reading defines various terms and methods associated with representing solids.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Representing Solids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Representing Solids” (HTML)
Instructions: Please click on the link above and complete questions 1–10 (“Lesson Exercises Pages 681–683 in the textbook). These questions will provide you with the opportunity to apply properties of representing solids. The solutions to these problems are located in the “Answers” section (starting on page 683 of the textbook).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Representing Solids”

10.3 Prisms
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Prisms”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Prisms” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the surface area and volume of prisms. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the surface area and volume of various prisms.
Reading these sections, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Prisms”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Prisms” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–20. These exercises will provide you with the opportunity to apply the formulas for surface area and volumes of prisms. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Prisms Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Prisms”

10.4 Cylinders
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cylinders”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cylinders” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the surface area and volume of cylinders. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the surface area and volume of various cylinders.
Reading these sections, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cylinders”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cylinders” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–16. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of cylinders. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Cylinders Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cylinders”

10.5 Pyramids
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pyramids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pyramids” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the surface area and volume of pyramids. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the surface area and volume of various pyramids.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pyramids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pyramids” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–19. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of pyramids. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Pyramids Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Pyramids”

10.6 Cones
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cones”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cones” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the surface area and volume of cones. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the surface area and volume of various cones.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cones”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cones” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–9 and 12–16. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of cones. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Cones Solutions” (PDF).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Cones”

10.7 Spheres
 Assessment: Khan Academy’s “Solid Geometry”
Link: Khan Academy’s “Solid Geometry” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on surface area and volume. You can review the concepts associated with these questions with the content in subunits 10.310.7. Determine if the given angle is acute, right, or obtuse using the interactive protractor. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This resource is licensed under a Creative Commons AttributionShareAlike License 3.0. It is attributed to the Khan Academy.  Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Spheres”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Spheres” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the surface area and volume of spheres. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the surface area and volume of various spheres.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Spheres”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Spheres” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 2–19. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of spheres. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Spheres Solutions” (PDF).
This activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Assessment: Khan Academy’s “Solid Geometry”

10.8 Composite Solids
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Composite Solids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Composite Solids” (HTML and YouTube)
Instructions: Please click on the link above and take notes as you watch the videos to learn about the surface area and volume of composite solids. Then, read the “Guidance,” “Vocabulary,” and “Guided Practice” sections. This section provides examples of finding the surface area and volume of various composite solids.
Reading the material, watching the videos, and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Composite Solids”
Link: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Composite Solids” (HTML)
Instructions: Please click on the link above, scroll down to the “Practice” section, and complete exercises 1–11 and 13–15. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of composite solids. You may also access the material in PDF, mobi, and ePub format by clicking on the appropriate link under “Download,” if you choose to create a free account. Once you have completed the exercises, check your answers against the Saylor Foundation’s “Composite Solids Solutions” (PDF).
This activity should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: CK12 Flexbook: Victor Cifarelli et al.’s Geometry: “Composite Solids”

Final Exam
 Final Exam: The Saylor Foundation’s “RWM103 Final Exam”
Link: The Saylor Foundation’s “RWM103 Final Exam”
Instructions: You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Final Exam: The Saylor Foundation’s “RWM103 Final Exam”